Are there directions associated with equipotential lines

Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth. A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Because a conductor is an equipotential, it can replace any equipotential surface.

For example, in Figure 1 a charged spherical conductor can replace the point charge, and the electric field and potential surfaces outside of it will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its center.

Figure 2 shows the electric field and equipotential lines for two equal and opposite charges. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines.

Conversely, given the equipotential lines, as in Figure 3 a , the electric field lines can be drawn by making them perpendicular to the equipotentials, as in Figure 3 b. One of the most important cases is that of the familiar parallel conducting plates shown in Figure 4. Between the plates, the equipotentials are evenly spaced and parallel. The same field could be maintained by placing conducting plates at the equipotential lines at the potentials shown.

An important application of electric fields and equipotential lines involves the heart. The heart relies on electrical signals to maintain its rhythm. The movement of electrical signals causes the chambers of the heart to contract and relax. When a person has a heart attack, the movement of these electrical signals may be disturbed.

An artificial pacemaker and a defibrillator can be used to initiate the rhythm of electrical signals. An artificial pacemaker and a defibrillator can be used to initiate the rhythm of electrical signals.

The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart. An electrocardiogram ECG measures the small electric signals being generated during the activity of the heart. Play around with this simulation to move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more.

If two points are at the same potential, are there any electric field lines connecting them? Suppose you have a map of equipotential surfaces spaced 1. What do the distances between the surfaces in a particular region tell you about the strength of the in that region? Is the electric potential necessarily constant over the surface of a conductor? Under electrostatic conditions, the excess charge on a conductor resides on its surface.

Does this mean that all of the conduction electrons in a conductor are on the surface? It depends on where the zero reference for potential is. Though this might be unusual. Two very large metal plates are placed 2. Consider one plate to be at 12 V, and the other at 0 V.

A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of. Can you explain why without any calculations? Does the location of your reference point matter? A metallic sphere of radius 2. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5. Now, a charge of is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell.

If potential is zero at infinity, what is the potential of a the spherical shell, b the sphere, c the space between the two, d inside the sphere, and e outside the shell? Two large charged plates of charge density face each other at a separation of 5. A long cylinder of aluminum of radius R meters is charged so that it has a uniform charge per unit length on its surface of.

Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude The plates are 1. What is the potential difference between the plates? The surface charge density on a long straight metallic pipe is. What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of 2 a. Concentric conducting spherical shells carry charges Q and — Q , respectively. The inner shell has negligible thickness.

What is the potential difference between the shells? In the region , and E is zero elsewhere; hence, the potential difference is. Shown below are two concentric spherical shells of negligible thicknesses and radii and The inner and outer shell carry net charges and respectively, where both and are positive.

What is the electric potential in the regions a b and c. A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges Q and — Q , respectively. Assuming that the length L of both conductors is much greater than a or b , what is the potential difference between the two conductors? From previous results , note that b is a very convenient location to define the zero level of potential:.

Skip to content Electric Potential. Learning Objectives By the end of this section, you will be able to: Define equipotential surfaces and equipotential lines Explain the relationship between equipotential lines and electric field lines Map equipotential lines for one or two point charges Describe the potential of a conductor Compare and contrast equipotential lines and elevation lines on topographic maps.

An isolated point charge Q with its electric field lines in red and equipotential lines in black. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines.

Why are no directions indicated on equipotential lines? Potential energy is a scalar, not a vector, quantity. Since no work is done in moving a charge over an equipotential surface, it follows that the electric field lines of force of force must charge over an equipotential surface, it follows that the electric field lines of force must be everywhere perpendicular to the equipotential surfaces.

Equipotential lines: point charge The equipotential lines are therefore circles and a sphere centered on the charge is an equipotential surface. The dashed lines illustrate the scaling of voltage at equal increments — the equipotential lines get further apart with increasing r. Last Updated: 15 days ago — Co-authors : 13 — Users : 9. Save my name, email, and website in this browser for the next time I comment.

Notify me of follow-up comments by email. Notify me of new posts by email. Home Answers About. Sign in. Forgot your password? Get help. Password recovery. Home English Why are there no arrows drawn for the equipotential lines? English General Lifestyle.

Read the full answer Equipotential lines at different potentials can never cross either. Figure 1. An isolated point charge Q with its electric field lines in blue and equipotential lines in green. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines.

Work is needed to move a charge from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case. It is important to note that equipotential lines are always perpendicular to electric field lines. Thus the work is. Work is zero if force is perpendicular to motion.

Force is in the same direction as E, so that motion along an equipotential must be perpendicular to E. More precisely, work is related to the electric field by. Note that in the above equation, E and F symbolize the magnitudes of the electric field strength and force, respectively. In other words, motion along an equipotential is perpendicular to E.

One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor.

This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow. One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding.

Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth. A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding.

Because a conductor is an equipotential, it can replace any equipotential surface.